How do you use solve #x^2 - 10x + 8 = 0#?

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Answer 1 · 2016-03-03T23:30:45

Complete the square and use the difference of squares identity to find:

#x = 5+-sqrt(17)#

The difference of squares identity can be written:

#a^2-b^2 = (a-b)(a+b)#

We use this with #a=(x-5)# and #b=sqrt(17)# below.

Complete the square then use the above as follows:

#0 = x^2-10x+8#

#=x^2-10x+25-17#

#=(x-5)^2-(sqrt(17))^2#

#=((x-5)-sqrt(17))((x-5)+sqrt(17))#

#=(x-5-sqrt(17))(x-5+sqrt(17))#

Hence: #x=5+-sqrt(17)#